Pushing down on the piston causes an increase in pressure and a decrease in the volume of the gas in the cylinder. This is BEST explained by the fact that

pressure and volume are inversely proportional for a gas when temperature is held constant.

pushing down on the piston decreases the amount of space available for the gas molecules to move, leading to more frequent and intense collisions between the gas molecules and the walls of the cylinder. This increased number of collisions results in a higher pressure of the gas. Additionally, as the volume of the cylinder decreases, the gas molecules become more confined, leading to a decrease in the volume of the gas.

the volume and pressure of a gas are inversely related according to Boyle's Law. Boyle's Law states that at a constant temperature, the pressure of a gas is inversely proportional to its volume.

To understand why pushing down on the piston causes an increase in pressure and a decrease in volume, we need to consider the mechanics of a piston-cylinder system. This system is commonly used to understand the behavior of gases.

When a force is applied to the piston by pushing it down, the volume of the gas in the cylinder decreases. This reduction in volume leads to the gas molecules being compressed into a smaller space, resulting in an increase in the number of collisions between the gas molecules and the walls of the cylinder. These collisions exert a greater force against the walls, thereby increasing the pressure.

On the other hand, when the piston is moved upwards, the volume of the gas increases. As a result, the gas molecules have more space to move around, reducing the frequency of collisions with the walls. Consequently, the pressure of the gas decreases.

Therefore, the increase in pressure and decrease in volume when pushing down on the piston can be explained by Boyle's Law, which states that as the volume of a gas decreases, the pressure of the gas increases.